Problem: Simplify the following expression: $z = \dfrac{7a}{6} - \dfrac{a}{9}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $6$ and $9$ $\lcm(6, 9) = 18$ $ z = \dfrac{3}{3} \cdot \dfrac{7a}{6} - \dfrac{2}{2} \cdot \dfrac{a}{9} $ $z = \dfrac{21a}{18} - \dfrac{2a}{18}$ $z = \dfrac{21a -2a}{18}$ $z = \dfrac{19a}{18}$